Question

The resistance of the wire in a heater at room temperature is 65 Ω. When the heater is connected to a 220 V supply the current settles after a few seconds to 2.8 A. What is the steady temperature of the wire? (Temperature coefficient of resistance α = 1.70 × 10^-4 °C^-1)
1. 955°C
2. 1055°C
3. 1155°C
4. 1258°C

Answer 1

Correct Answer - Option 4 : 1258°C

Concept:

The resistance of the conductor changes when the temperature of that conductor changes.

New resistance is given by

\({{R}_{t}}={{R}_{0}}\left( 1+\alpha \text{ }\!\!\Delta\!\!\text{ }T \right)\)

Where Rt = the resistance of conductor after temperature changes

R0 = the resistance of conductor before temperature changes

α = temperature coefficient

ΔT = final temperature – initial temperature

Calculation:

Given;

T₁ = 27°C, R₁ = 65 Ω

\({R_2} = \frac{{Supply\;voltage}}{{Steady\;current}} = \frac{{220}}{{2.8}} = 78.6\;{\rm{\Omega }}\) 

Now, using the relation

R₂ = R₁ [1 + α (T₂ – T₁)]

\({T_2} - {T_1} = \frac{{{R_2} - {R_1}}}{{{R_1}}} \times \frac{1}{\alpha }\)

\( = \frac{{78.6 - 65}}{{65}} \times \frac{1}{{1.7\; \times\; {{10}^{ - 4}}}}\)

T₂ – T₁ = 1231

T₂ = 1231 + T₁

= 1231 + 27 = 1258°C